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这里我们介绍一种简易的量地法。由于在进行测量的过程中必须量出互相垂直的形如“+”字的两条线段的长度,因此,一般的管它叫做“+字量地法”。对于象下面一些形状的田地,在实际测量时只要分别测得互相垂直的两条线段AB和CD的长度就可以了。显然,它们的根据就是几何中的求积公式。事实上,对于三角形来说,图中CD就是它两边中点的连线,等于底边的一半,于是,AB·CD就是三角形的面积;对于梯形来说,CD就是两腰中点的连线,等于两底和的一半,于是AB·CD也就是梯形的面积了,对于矩形,它的面积显然是AE·CD。对于形状不规则的田地,我们可以对它适当的分割,把它分成若干块形状近似于三角形、矩形和梯形的各个部分。
Here we introduce a simple quantitative method. Since the lengths of the two line segments in the shape of “+” must be measured perpendicular to each other in the process of measurement, the general pipe is called “+word size ground method”. For fields like the following shapes, it is sufficient to measure the lengths of the two line segments AB and CD perpendicular to each other during actual measurement. Obviously, their basis is the quadrature formula in geometry. In fact, for a triangle, the CD in the figure is the line connecting the midpoints of its two sides, which is equal to half of the bottom edge. Therefore, AB·CD is the area of the triangle; for the trapezoid, CD is the line connecting the midpoints of the two waists. , which is equal to half the sum of the two bottoms, so ABCD is also the area of the trapezoid. For the rectangle, its area is obviously AE·CD. For an irregularly shaped field, we can divide it properly and divide it into blocks of shapes that approximate the triangles, rectangles, and trapezoids.